Washington (CNN) - With senior officials saying he's edging closer to announcing his pick for the Supreme Court, President Obama interviewed federal judge Diane Wood at the White House on Tuesday, according to two sources familiar with the process.

Vice President Biden also conducted a separate one-on-one interview with Wood on Tuesday, according to the sources familiar with the process. A source close to Wood told CNN she had abruptly canceled her Tuesday afternoon class at the University of Chicago.

In addition to her judgeship, the 59-year-old Wood teaches a Civil Procedure class part-time. She was a finalist for the high court vacancy last year and had also met with Obama personally for the job that ultimately went to Justice Sonia Sotomayor.

This time around, Obama has now held four one-on-one meetings with potential nominees to succeed retiring Justice John Paul Stevens, and the sources said there could be other meetings.

Sources familiar with the process are privately suggesting Obama's pick is likely to be publicly announced early next week, but the sources stressed it's still possible that the pick will be revealed this week.

Pressed by reporters on Tuesday, White House Press Secretary Robert Gibbs was vague about the timing. "I will just simply say that when the President informs us that he's made that decision, we will notify you as to when that announcement will be," he said. "I'm not going to every day rule in or rule out when that might be."

Obama has said publicly he intends to nominate a candidate to succeed Stevens by the end of May, so that the Senate can complete the confirmation process in time for the new Supreme Court session in the fall.